Standard Class Standard_LambdaJulia

Object common:Generic common:Formula common:DivergentFormula Standard:Standard_LambdaJulia

class
DivergentFormula:Standard_LambdaJulia

Object version of LambdaJulia in Standard.ufm. Alternative Julia set that iterates the classical Logistics equation using complex numbers. All Julia sets created with this type can be recreated with the classical Julia set, but the parameters work differently, and the corresponding Mandelbrot set is different, too. Originally written by Damien M. Jones.

Ultra Fractal Source
class Standard_LambdaJulia(common.ulb:DivergentFormula) {
;
; Object version of LambdaJulia in Standard.ufm.
;
; Alternative Julia set that iterates the classical Logistics
; equation using complex numbers. All Julia sets created with
; this type can be recreated with the classical Julia set,
; but the parameters work differently, and the corresponding
; Mandelbrot set is different, too.
;
; Originally written by Damien M. Jones.
;
public:
complex func Init(complex pz)
return pz
endfunc

complex func Iterate(complex pz)
return @seed * pz * (1 - pz) ^ (@p_power - 1)
endfunc

default:
title = "Lambda (Julia)"
helpfile = "Uf*.chm"
helptopic = "Html/formulas/standard/lambda.html"
param seed
caption = "Julia Seed"
default = (1,0)
hint = "Use this parameter to create many different Julia sets. A good \
way to set this parameter is with the Eyedropper or Explore features."
endparam
param p_power ; Overrides p_power from Formula
caption = "Exponent"
default = (2,0)
hint = "This parameter sets the exponent for the Julia formula. \
Increasing the real part to 3, 4, and so on, will multiply the \
symmetry of the Julia figure. Non-integer real values and non-zero \
imaginary values will create distorted Julia fractals. Use (2, 0) \
for the standard Julia set."
endparam
param p_bailout ; Overrides p_bailout from DivergentFormula
caption = "Bailout"
default = 1.0e20
exponential = true
hint = "This parameter defines how soon an orbit bails out while \
iterating. Larger values give smoother outlines; values around 4 \
give more interesting shapes around the set. Values less than 4 \
will distort the fractal."
endparam
}

Constructor Summary
Standard_LambdaJulia()

Method Summary
complex Init(complex pz)
Set up for a sequence of values
complex Iterate(complex pz)
Produce the next value in the sequence

Methods inherited from class common:DivergentFormula
GetUpperBailout, IsBailedOut

Methods inherited from class common:Formula
GetLowerBailout, GetPrimaryExponent

Methods inherited from class common:Generic
GetParent

Methods inherited from class Object

Constructor Detail

Standard_LambdaJulia

public Standard_LambdaJulia()
Method Detail

Init

public complex Init(complex pz)
Description copied from class: DivergentFormula
Set up for a sequence of values

This function will be called at the beginning of each sequence of values (e.g. at the beginning of each fractal orbit).

Overrides:
Init in class DivergentFormula
Parameters:
pz - seed value for the sequence; for a normal fractal formula, this will be #pixel
Returns:
first value in the sequence; this corresponds to #z in a fractal formula

Iterate

public complex Iterate(complex pz)
Description copied from class: Formula
Produce the next value in the sequence

As long as the sequence has not bailed out, this function will be continually called to produce sequence values.

Overrides:
Iterate in class Formula
Parameters:
pz - previous value in the sequence; corresponds to #z in a fractal formula. Note that you should always use this value for computing the next iteration, rather than a saved value, as the calling code may modify the returned value before passing it back to the next Iterate() call.
Returns:
the next value in the sequence